Large deviations, Gibbs measures and closed orbits for hyperbolic flows
To the results of Bowen and Parry on spatial distribution of closed orbits and Gibbs measures for hyperbolic flows by large deviation type we add estimates on the exceptional closed orbits in these distribution results (Theorem 1). As a special case, we can apply these results to closed orbits of geodesic flows on compact negatively curved manifolds and the Liouville measure (Corollary 2). As an application we use these to study certain selective zeta functions whose definition involves only closed orbits which support invariant probability measures lying in a weak star closed set \({\mathcal K}\) (Theorem 2 and Proposition 5).
scientific article; zbMATH DE number 856561
scientific article